Three positive whole numbers have a mean of 6. What is the greatest possible range of the three numbers?

The mean is the total of the numbers divided by how many numbers there are. So to find the mean of six, we need to add three numbers together, divide those three numbers by three and get six. This sounds tricky but when I teach you an easy method, you'll find it so much easier! Step one: Write out a+b+c divided by the number in the question (three) = the mean (six). Step two: Times both sides by three to get rid of the division so you get a+b+c=18 Step three: work out the two smallest numbers and the one biggest number you can use to make 18. 1+1+16=18. Step three: work out the range between 1 and 16. you can do this by taking one away from sixteen or by making a number line and counting each hop from 1 to 16 (but this might take a while in the exam!).

The greatest possible range is 15.